Armature: Align and rotate bones at the same time around center point
The transformation constraint can be used to do what you want. This constraint allows you to proportionally move a bone based on another bone, the advantage is that the movement doesn't have to match the bone being moved.



To setup, add two new bones, one as a control for the upper movement, the other for the lower. In the attached sample I also added a limit location constraint so that these can only be moved within the range of motion that works for this.

Next align the roll of each bone (in edit mode) so that the x-axis is aligned to the direction you want the bone to rotate, this allows a single axis rotation to be used and lets us copy the same settings to each bone.



Next setup one upper bone.


Add a transformation constraint.
Select the armature and bone that will control it. 
Set the source Y location range.
Set the destination mapping so that the source Y controls the destination Z.
Set the destination Z location range to suit.
Set the space options to local space, this makes it use the bones axes, not world axes.




Now setup one lower bone.


Add a transformation constraint.
Select the armature and bone that will control it. 
Set the source Y location range.
Set the destination mapping so that the source Y controls the destination X.
Set the destination X rotation range to suit.
Set the space options to local space.




Add a second constraint to the lower bone, set this one to use the second control bone and set the rotation as the negative of the previous one.

Once you have one leg that moves correctly when you move a control bone, copy the same constraints to the other bones. To make this easier, enable the copy attributes addon, this is included with blender. Select all the upper bones with the finished bone being the last selected, now press &#9096; CtrlC->Copy Bone Constraints. Repeat with the lower bones.

Note that armatures have their own layer system, you can move all the arm bones to another armature layer so they can be hidden, leaving just the two control bones as visible while animating.